A parametric transfer matrix approach to fault-identification filter design and threshold selection

By employing a transfer matrix approach we develop straightforward design procedures to construct a fault-identification filter (FIDF) to achieve failure detection and isolation. Furthermore, we derive the necessary and sufficient conditions for the synthesis of the FIDF. The condition entails a parametrization of the set of all achievable diagonal fault/residual maps and the set of all existing FIDFs. Since the diagnostic performance of the FIDF is influenced significantly by the model uncertainty, we present a framework for analysing the FIDF by incorporating modelling errors. Consequently, a criterion to determine an adequate threshold for the FIDF based on robust control theory is derived. Examples are used to illustrate the validity of this approach